We describe a powerful
theoretical approach to studying electronic band structures, which associates
them with elements of a vector space. The set of consistent band structures in
a space group can then be expanded in terms of a small set of basis vectors. We
calculate the dimension of this vector space, and the necessary electron
fillings to obtain band insulators in all magnetic space groups.

Selection rules impose geometrical constraints on the interactions of light and matter. Inparticular, an emitter with a well-defined orientation will emit photons of a characteristicpolarization and wavevector distribution, even as viewed in the far field. Knowledge of thesedistributions can be leveraged to enhance a number of state-of-the-art microscopy techniques. Inthe first part of the talk I will discuss such an approach to single-molecule localizationmicroscopy, relevant for single-molecule tracking and super-resolution imaging. It is known that

Microcavity exciton-polaritons
provide a unique photonic platform that manifests non-equilibrium quantum
orders. It combines strong nonlinearity and rich many-body physics of matter
with robust coherence and ready accessibility of light, allowing diverse
quantum phenomena at high temperature, on a photonic chip. To go beyond 2D
condensation physics, it becomes important to control the fundamental
properties of polaritons without destroying the quantum orders.

The gut governs digestion and nutrient
absorption, is a promising target for drug delivery, and teems with
micro-organisms that can have remarkably strong effects on host health. Despite
its importance, however, little is known about how the structure and function
of the gut are influenced by many of the soft materials that transit through it
regularly.

Research in microbial
physiology has traditionally focused on understanding biochemical pathways and,
more recently, on elucidating the surprisingly complex structure of microbial
cytoplasm. On the other hand, the whether mechanical forces also play a
role in controlling sub-cellular processes in microbes has been
overlooked. I will highlight several novel paradigms by which
microbes use mechanical (and electrical) factors as signals to control cell
growth, division, and survival, and highlight how the remarkable mechanical
properties of the cells are critical for these p

Topological insulators are solid-state materials whose
transport properties are immune to defects and disorder due to underlying topological order. Perhaps the first such
phenomenon was the quantum Hall effect, wherein the Hall conductivity is
quantized and hence extremely robust. In this talk, I will present the
experimental observation of the topological protection of the transport of photons (rather than electrons
in the solid state) in complex dielectric structures. I will then present
the obser